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Solution for Differential Coefficient of Sec Sec ( Tan − 1 X ) is (A) X 1 + X 2 (B) X √ 1 + X 2 - CBSE (Commerce) Class 12 - Mathematics

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Question

Differential coefficient of sec

\[\sec \left( \tan^{- 1} x \right)\] is
(a)  \[\frac{x}{1 + x^2}\]
(b)  \[x \sqrt{1 + x^2}\]
(c) \[\frac{1}{\sqrt{1 + x^2}}\]
(d) \[\frac{x}{\sqrt{1 + x^2}}\]

 

Solution

(d) \[\frac{x}{\sqrt{1 + x^2}}\] 

\[\text{We have, y } = \sec\left( \tan^{- 1} x \right)\]
\[ \Rightarrow \frac{dy}{dx} = \sec\left( \tan^{- 1} x \right) \tan\left( \tan^{- 1} x \right) \times \frac{d}{dx}\left( \tan^{- 1} x \right)\]
\[ \Rightarrow \frac{dy}{dx} = \sec\left( \tan^{- 1} x \right) \tan\left( \tan^{- 1} x \right) \times \frac{1}{\sqrt{1 + x^2}}\]
\[ \Rightarrow \frac{dy}{dx} = y\left( \frac{x}{\sqrt{1 + x^2}} \right)\]
\[ \Rightarrow \frac{dy}{dx} = \left( \frac{x}{\sqrt{1 + x^2}} \right) y\]

This is the equation of differential equation which have coefficient

\[\frac{x}{\sqrt{1 + x^2}}\]

  Is there an error in this question or solution?

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Solution Differential Coefficient of Sec Sec ( Tan − 1 X ) is (A) X 1 + X 2 (B) X √ 1 + X 2 Concept: Simple Problems on Applications of Derivatives.
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